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Properties

Label 276.2.a
Level $276$
Weight $2$
Character orbit 276.a
Rep. character $\chi_{276}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 276.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(276))\).

Total New Old
Modular forms 54 4 50
Cusp forms 43 4 39
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(23\)FrickeDim
\(-\)\(+\)\(+\)$-$\(2\)
\(-\)\(-\)\(-\)$-$\(2\)
Plus space\(+\)\(0\)
Minus space\(-\)\(4\)

Trace form

\( 4 q + 4 q^{5} + 4 q^{7} + 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{5} + 4 q^{7} + 4 q^{9} + 8 q^{13} + 4 q^{15} + 12 q^{17} - 4 q^{19} - 4 q^{21} + 12 q^{25} + 16 q^{29} - 8 q^{31} - 16 q^{35} - 16 q^{37} - 8 q^{39} - 8 q^{41} - 12 q^{43} + 4 q^{45} - 16 q^{47} + 4 q^{49} - 4 q^{51} + 4 q^{53} - 16 q^{55} - 12 q^{57} - 16 q^{59} + 4 q^{63} - 16 q^{65} - 28 q^{67} + 4 q^{69} + 8 q^{73} - 8 q^{75} - 16 q^{77} + 20 q^{79} + 4 q^{81} - 16 q^{83} + 8 q^{87} + 12 q^{89} - 8 q^{93} + 16 q^{95} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(276))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 23
276.2.a.a 276.a 1.a $2$ $2.204$ \(\Q(\sqrt{10}) \) None \(0\) \(-2\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+(2-\beta )q^{7}+q^{9}+4q^{13}+\cdots\)
276.2.a.b 276.a 1.a $2$ $2.204$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(2+\beta )q^{5}+\beta q^{7}+q^{9}-4\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(276))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(276)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 2}\)